Solve the system of inequalities by graphing.
$\begin{array}{l}
y \geq 3 \\
y < 9
\end{array}$
We are given a system of two inequalities involving the variable \(y\):
The goal is to solve and represent this system on a coordinate plane. The first inequality, \(y \geq 3\), describes all points where the vertical position is at least 3. Since the inequality is "greater than or equal to," we include the line \(y=3\). The second inequality, \(y < 9\), describes all points where the vertical position is less than 9. Since the inequality is "strictly less than," we exclude the line \(y=9\). Taken together, the solution represents the set of all points \((x, y)\) such that the y-coordinate is between 3 (inclusive) and 9 (exclusive).
To visualize this, we look at the Cartesian plane. The condition \(y \geq 3\) covers the region on and above the horizontal line \(y=3\). The condition \(y < 9\) covers the region below the horizontal line \(y=9\). The intersection of these two regions is the infinite strip of the plane bounded by these two horizontal lines.
The solution to the system \(y \geq 3\) and \(y < 9\) is the horizontal strip of the plane consisting of all points \((x, y)\) where the y-coordinate satisfies \(3 \leq y < 9\). On a graph, this is shown as a solid line at \(y=3\), a dashed line at \(y=9\), and the shaded area between them. Any point with a y-coordinate in this interval is a valid solution, regardless of its x-coordinate. Thus, the solution is \(\boxed{3 \leq y < 9}\).
Imagine you are designing a storage shelf in a pantry. You want to place items that need to be within a certain height range to be easily accessible. If the bottom shelf is at 3 feet from the ground and the next level is at 9 feet, you can place your items anywhere between these two heights. The condition \(y \geq 3\) and \(y < 9\) perfectly models this accessible space, ensuring your items are reachable and safe within the 3-foot to 9-foot vertical interval.